
pip install pmdarima

Looking in indexes: https://pypi.org/simple, https://us-python.pkg.dev/colab-wheels/public/simple/
Collecting pmdarima
  Downloading pmdarima-2.0.1-cp37-cp37m-manylinux_2_17_x86_64.manylinux2014_x86_64.manylinux_2_28_x86_64.whl (1.8 MB)
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Collecting statsmodels>=0.13.2
  Downloading statsmodels-0.13.5-cp37-cp37m-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (9.9 MB)
     |████████████████████████████████| 9.9 MB 49.3 MB/s 
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Installing collected packages: statsmodels, pmdarima
  Attempting uninstall: statsmodels
    Found existing installation: statsmodels 0.12.2
    Uninstalling statsmodels-0.12.2:
      Successfully uninstalled statsmodels-0.12.2
Successfully installed pmdarima-2.0.1 statsmodels-0.13.5


import numpy as np
import pandas as pd
import plotly.express as px
import matplotlib.pyplot as plt

import sklearn as sk
from sklearn import impute
from sklearn import preprocessing
from pmdarima.arima import auto_arima
from statsmodels.tsa.stattools import adfuller
import sklearn.externals
import joblib
from sklearn.model_selection import TimeSeriesSplit
from sklearn.impute import KNNImputer
from statsmodels.graphics.tsaplots import plot_acf
from statsmodels.graphics.tsaplots import plot_pacf
import sklearn.preprocessing
import math

import sklearn.externals
import joblib
import plotly.graph_objects as go
from sklearn import metrics

import statsmodels.api as sm
import statsmodels.tsa.stattools as ts
from statsmodels.tsa.statespace.sarimax import SARIMAX


%matplotlib inline


import plotly.io as pio
pio.renderers.default='notebook'


from google.colab import drive
drive.mount('/content/drive')

Mounted at /content/drive


df = pd.read_csv("/content/drive/Shareddrives/Mineria /Temperatura1.csv", sep=';', header=0, decimal = ',')
Fecha = pd.date_range(start='2017-01-01', end='2021-12-31', freq='D')
df['Fecha'] = Fecha
df = df.set_index('Fecha')

print(df[pd.isnull(df.ValorObservado)])
print('En total hay' ,
      str(df['ValorObservado'].isnull().sum()) ,
      'valores sin información')
print('Correspondientes al {:.3f}% del total'
      .format(df['ValorObservado'].isnull().sum()*100/len(df)))

            ValorObservado
Fecha                     
2017-08-12             NaN
2017-12-24             NaN
2019-09-15             NaN
2019-09-16             NaN
2019-09-17             NaN
2020-11-12             NaN
2021-01-05             NaN
2021-01-06             NaN
2021-01-07             NaN
2021-01-08             NaN
2021-08-18             NaN
2021-08-20             NaN
2021-12-05             NaN
En total hay 13 valores sin información
Correspondientes al 0.712% del total


#Imputación de Valores usando el vecino más cercano
imput = KNNImputer(n_neighbors=5, weights="uniform")

# Ajustamos el modelo e imputamos los missing values
imput.fit(df[['ValorObservado']])
df['ValorObservado'] = imput.transform(df[['ValorObservado']]).ravel()
print()
print("Valores pérdidos en ValorObservado: " , 
      str(df['ValorObservado'].isnull().sum()))

Valores pérdidos en ValorObservado:  0


fig = px.line(df, x=df.index, y="ValorObservado")
fig.update_xaxes(title_text="Fecha")
fig.show()


train_size = len(df[:1465])
test_size = len(df) - train_size
X_train, X_test = df.iloc[0:train_size], df.iloc[train_size:len(df)]
len_train = len(X_train)
len_test = len(X_test)
seq_len = 20
print(len_train, len_test)

1465 361


adfstat, pvalue, critvalues, resstore=adfuller(X_train,regression="nc",maxlag=9,store=True,regresults=True)####maxlag es importante
print(resstore.resols.summary())

resultadoadf=adfuller(X_train,regression="nc")
print('ADF Statistic: %f' % resultadoadf[0])
print('P-value: %f' % resultadoadf[1])
for key, value in resultadoadf[4].items():
    print('\t%s: %.3f' % (key, value))

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:824: FutureWarning:

trend 'nc' has been renamed to 'n' after 0.14 is released. Use 'n' now to avoid this warning.

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.136
Model:                            OLS   Adj. R-squared (uncentered):              0.131
Method:                 Least Squares   F-statistic:                              25.38
Date:                Wed, 23 Nov 2022   Prob (F-statistic):                    7.64e-41
Time:                        01:32:44   Log-Likelihood:                         -1409.2
No. Observations:                1456   AIC:                                      2836.
Df Residuals:                    1447   BIC:                                      2884.
Df Model:                           9                                                  
Covariance Type:            nonrobust                                                  
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
x1            -0.0006      0.001     -0.400      0.689      -0.003       0.002
x2            -0.3579      0.026    -13.586      0.000      -0.410      -0.306
x3            -0.2746      0.028     -9.855      0.000      -0.329      -0.220
x4            -0.1894      0.029     -6.590      0.000      -0.246      -0.133
x5            -0.1459      0.029     -4.948      0.000      -0.204      -0.088
x6            -0.0908      0.030     -3.068      0.002      -0.149      -0.033
x7            -0.0812      0.029     -2.770      0.006      -0.139      -0.024
x8            -0.0980      0.028     -3.447      0.001      -0.154      -0.042
x9            -0.0786      0.027     -2.936      0.003      -0.131      -0.026
==============================================================================
Omnibus:                      129.718   Durbin-Watson:                   1.995
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              780.948
Skew:                           0.109   Prob(JB):                    2.63e-170
Kurtosis:                       6.581   Cond. No.                         33.0
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:824: FutureWarning:

trend 'nc' has been renamed to 'n' after 0.14 is released. Use 'n' now to avoid this warning.

ADF Statistic: -0.361488
P-value: 0.552031
	1%: -2.567
	5%: -1.941
	10%: -1.617


dif_dataset=X_train.diff(periods=1)
dif_dataset=dif_dataset.dropna()

fig = px.line(dif_dataset, x=dif_dataset.index, y="ValorObservado")
fig.update_xaxes(title_text="Fecha")
fig.show()


adfstat, pvalue, critvalues, resstore=adfuller(dif_dataset,regression="nc",maxlag=9,store=True,regresults=True)####maxlag es importante
print(resstore.resols.summary())

resultadoadf=adfuller(dif_dataset,regression="nc")
print('ADF Statistic: %f' % resultadoadf[0])
print('P-value: %f' % resultadoadf[1])
for key, value in resultadoadf[4].items():
    print('\t%s: %.3f' % (key, value))

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:824: FutureWarning:

trend 'nc' has been renamed to 'n' after 0.14 is released. Use 'n' now to avoid this warning.

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:824: FutureWarning:

trend 'nc' has been renamed to 'n' after 0.14 is released. Use 'n' now to avoid this warning.

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                      y   R-squared (uncentered):                   0.656
Model:                            OLS   Adj. R-squared (uncentered):              0.654
Method:                 Least Squares   F-statistic:                              275.3
Date:                Wed, 23 Nov 2022   Prob (F-statistic):                        0.00
Time:                        01:32:45   Log-Likelihood:                         -1404.3
No. Observations:                1454   AIC:                                      2829.
Df Residuals:                    1444   BIC:                                      2882.
Df Model:                          10                                                  
Covariance Type:            nonrobust                                                  
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
x1            -2.5418      0.155    -16.417      0.000      -2.845      -2.238
x2             1.1798      0.146      8.060      0.000       0.893       1.467
x3             0.8967      0.136      6.616      0.000       0.631       1.162
x4             0.6980      0.123      5.657      0.000       0.456       0.940
x5             0.5443      0.110      4.938      0.000       0.328       0.760
x6             0.4437      0.096      4.628      0.000       0.256       0.632
x7             0.3475      0.080      4.332      0.000       0.190       0.505
x8             0.2290      0.064      3.604      0.000       0.104       0.354
x9             0.1205      0.045      2.648      0.008       0.031       0.210
x10            0.0680      0.027      2.533      0.011       0.015       0.121
==============================================================================
Omnibus:                      130.012   Durbin-Watson:                   1.992
Prob(Omnibus):                  0.000   Jarque-Bera (JB):              776.875
Skew:                           0.122   Prob(JB):                    2.01e-169
Kurtosis:                       6.573   Cond. No.                         29.1
==============================================================================

Notes:
[1] R² is computed without centering (uncentered) since the model does not contain a constant.
[2] Standard Errors assume that the covariance matrix of the errors is correctly specified.
ADF Statistic: -12.369790
P-value: 0.000000
	1%: -2.567
	5%: -1.941
	10%: -1.617


graph1=plot_acf(dif_dataset,lags=60,adjusted=False)
graph2=plot_pacf(dif_dataset,lags=30,method='ldbiased')


auto = auto_arima(X_train, error_action='ignore',max_p=4,d=1,max_q=2,max_order=6,seasonal=True,information_criterion='bic')
auto.summary()


#modeloarima1=sm.tsa.SARIMAX(X_train, trend='n', order=(4,1,2))
#ajustearima1=modeloarima1.fit()
#print('ARIMA(4,1,2)')
#print(ajustearima1.summary())
#modeloarima2=sm.tsa.SARIMAX(X_train, trend='n', order=(4,1,1))
#ajustearima2=modeloarima2.fit()
#print('ARIMA(4,1,1)')
#print(ajustearima2.summary())
modeloarima3=sm.tsa.SARIMAX(X_train, trend='n', order=(3,1,3))
ajustearima3=modeloarima3.fit()
print('ARIMA(4,1,3)')
print(ajustearima3.summary())

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/base/tsa_model.py:471: ValueWarning:

No frequency information was provided, so inferred frequency D will be used.

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/base/tsa_model.py:471: ValueWarning:

No frequency information was provided, so inferred frequency D will be used.

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

ARIMA(4,1,3)
                               SARIMAX Results                                
==============================================================================
Dep. Variable:         ValorObservado   No. Observations:                 1465
Model:               SARIMAX(3, 1, 3)   Log Likelihood               -1401.741
Date:                Wed, 23 Nov 2022   AIC                           2817.483
Time:                        01:33:06   BIC                           2854.505
Sample:                    01-01-2017   HQIC                          2831.292
                         - 01-04-2021                                         
Covariance Type:                  opg                                         
==============================================================================
                 coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
ar.L1          0.3918      0.147      2.662      0.008       0.103       0.680
ar.L2          0.8434      0.191      4.409      0.000       0.468       1.218
ar.L3         -0.3137      0.090     -3.486      0.000      -0.490      -0.137
ma.L1         -0.7662      0.142     -5.390      0.000      -1.045      -0.488
ma.L2         -0.8691      0.229     -3.799      0.000      -1.317      -0.421
ma.L3          0.6415      0.121      5.283      0.000       0.404       0.879
sigma2         0.3962      0.009     44.679      0.000       0.379       0.414
===================================================================================
Ljung-Box (L1) (Q):                   0.02   Jarque-Bera (JB):               816.57
Prob(Q):                              0.88   Prob(JB):                         0.00
Heteroskedasticity (H):               0.85   Skew:                             0.13
Prob(H) (two-sided):                  0.08   Kurtosis:                         6.65
===================================================================================

Warnings:
[1] Covariance matrix calculated using the outer product of gradients (complex-step).

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals


ARIMA_mod=sm.tsa.SARIMAX(X_train, trend='n', order=(3,1,3))
ARIMA_model=ARIMA_mod.fit()

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/base/tsa_model.py:471: ValueWarning:

No frequency information was provided, so inferred frequency D will be used.

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/base/tsa_model.py:471: ValueWarning:

No frequency information was provided, so inferred frequency D will be used.

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals


#####Análisis de Residuales######
residuales=ARIMA_model.resid####Residuales no estandarizados

graf_resid=ARIMA_model.plot_diagnostics()
#plt.show()
## Hipótesis nula de no heterocedasticidad
ARIMA_model.test_heteroskedasticity(method='breakvar') #[Est. de prueba, p-valor]
## Hipótesis nula de normalidad
ARIMA_model.test_normality(method='jarquebera')
#1. Estadística de prueba
#2. El p valor
#3. Sesgo estimado de los datos
#4. Curtosis estimada
## Hipótesis nula indica que no se presenta correlación serial

array([[8.16568246e+002, 4.83568793e-178, 1.27794283e-001,
        6.64979988e+000]])


Res_estand=ajustearima3.standardized_forecasts_error.reshape(1465,)

##CUSUM
cum=Res_estand.cumsum()
N=len(Res_estand)
N
Af_cusum=0.948###Cuantil estadística cusum
LS=Af_cusum*math.sqrt(N)+2*Af_cusum*np.arange(1,N+1)/math.sqrt(N)
LI=-LS
plt.plot(cum)
plt.plot(LS,color='red')
plt.plot(LI,color='red')
plt.xlabel("t")
plt.ylabel("Cusm")
plt.title('Estadística Cusum')

Text(0.5, 1.0, 'Estadística Cusum')


#CUSUMQ
cumq=(Res_estand**2).cumsum()/sum(Res_estand**2)
co=0.13291####Valor del cuantil aproximado para cusumsq para n/2
LQS=co+np.arange(1,N+1)/N
LQI=-co+np.arange(1,N+1)/N
plt.plot(cumq)
plt.plot(LQS,color='red')
plt.plot(LQI,color='red')
plt.xlabel("t")
plt.ylabel("Cusm")
plt.title('Estadística Cusumsq')

Text(0.5, 1.0, 'Estadística Cusumsq')


## Rolling
from sklearn.metrics import mean_squared_error
val = df.values
size = len(df[:1465])
train, test = val[1:size], val[size:len(val)]
history = [x for x in train]
predicciones = list()
for t in range(len(test)):
	modelo = sm.tsa.statespace.SARIMAX(history, trend='n', order=(3,1,3))
	modelo_fit = modelo.fit(disp=0)
	output = modelo_fit.forecast()
	yhat = output[0]
	predicciones.append(yhat)
	obs = test[t]
	history.append(obs)
	print('Predicción=%f, Esperado=%f' % (yhat, obs))

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicción=12.048250, Esperado=11.939085

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicción=12.100327, Esperado=11.939085

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicción=11.915657, Esperado=11.939085

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicción=11.985208, Esperado=11.939085

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicción=11.850243, Esperado=13.904167


d=pd.DataFrame(predicciones)
d=d.set_index(df.index[len(X_train):])
d=pd.concat([d, X_test], axis=1)
d['ARIMA_Predict']=d[0]
joblib.dump(d,'/content/drive/Shareddrives/Mineria /ARIMA_Predict')

['/content/drive/Shareddrives/Mineria /ARIMA_Predict']


# plot y_train, y_test, and testPredict using plotly
fig = go.Figure()
fig.add_trace(
    go.Scatter(
        x=df.index[: len(X_train)],
        y=X_train['ValorObservado'],
        mode="lines",
        name="Entrenamiento",
    )
)
fig.add_trace(
    go.Scatter(
        x=df.index[len(X_train):],
        y=X_test['ValorObservado'],
        mode="lines",
        name="Prueba",
    )
)
fig.add_trace(
    go.Scatter(
        x=df.index[len(X_train):],
        y=d.ARIMA_Predict,
        mode="lines",
        name="Predicción",
    )
)
fig.update_xaxes(title_text="Fecha")
fig.update_yaxes(title_text="ValorObservado")
fig.show()


from sklearn.metrics import mean_squared_error
error = mean_squared_error(d.ValorObservado, d.ARIMA_Predict)
print('Test Score: %.2f RMSE' % (error))

Test Score: 0.68 RMSE


## Rolling
val = df.values
size = len(df[:1465])
train, test = val[1:size], val[size:len(val)]
history = [x for x in train]
predicciones = list()
for t in range(len(test)):
	modelo = sm.tsa.statespace.SARIMAX(history, trend='n', order=(3,1,3))
	modelo_fit = modelo.fit(disp=0)
	output = modelo_fit.forecast(5)
	yhat = output[4]
	predicciones.append(yhat)
	obs = test[t]
	history.append(obs)
	print('Predicción=%f, Esperado=%f' % (yhat, obs))

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/sarimax.py:966: UserWarning:

Non-stationary starting autoregressive parameters found. Using zeros as starting parameters.

/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/statespace/sarimax.py:978: UserWarning:

Non-invertible starting MA parameters found. Using zeros as starting parameters.

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicción=11.996235, Esperado=11.939085

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicción=11.924534, Esperado=11.939085

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicción=11.733528, Esperado=11.939085

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicción=11.809168, Esperado=11.939085

/usr/local/lib/python3.7/dist-packages/statsmodels/base/model.py:606: ConvergenceWarning:

Maximum Likelihood optimization failed to converge. Check mle_retvals

Predicción=11.703210, Esperado=13.904167


d=pd.DataFrame(predicciones)
d=d.set_index(df.index[len(X_train):])
d=pd.concat([d, X_test], axis=1)
d['ARIMA_Predict']=d[0]
joblib.dump(d,'/content/drive/Shareddrives/Mineria /ARIMA_Predict')

['/content/drive/Shareddrives/Mineria /ARIMA_Predict']


# plot y_train, y_test, and testPredict using plotly
fig = go.Figure()
fig.add_trace(
    go.Scatter(
        x=df.index[: len(X_train)],
        y=X_train['ValorObservado'],
        mode="lines",
        name="Entrenamiento",
    )
)
fig.add_trace(
    go.Scatter(
        x=df.index[len(X_train):],
        y=X_test['ValorObservado'],
        mode="lines",
        name="Prueba",
    )
)
fig.add_trace(
    go.Scatter(
        x=df.index[len(X_train):],
        y=d.ARIMA_Predict,
        mode="lines",
        name="Predicción",
    )
)
fig.update_xaxes(title_text="Fecha")
fig.update_yaxes(title_text="ValorObservado")
fig.show()


from sklearn.metrics import mean_squared_error
error = mean_squared_error(d.ValorObservado, d.ARIMA_Predict)
print('Test Score: %.2f RMSE' % (error))

Test Score: 0.84 RMSE

	coef	std err	z	P>\|z\|	[0.025	0.975]
ar.L1	1.2722	0.085	14.978	0.000	1.106	1.439
ar.L2	-0.3217	0.068	-4.762	0.000	-0.454	-0.189
ma.L1	-1.6551	0.077	-21.556	0.000	-1.806	-1.505
ma.L2	0.6597	0.075	8.826	0.000	0.513	0.806
sigma2	0.3975	0.009	44.704	0.000	0.380	0.415

Modelando la serie de la temperatura

Importación de Datos

Imputación a partir del vecino más cercano

Separación de datos entrenamiento y validación

Modelo ARIMA (p,d,q)

Prueba de Dickey Fuller

Gráficos de autocorrelación simple y parcial

Análisis de Residuales

Predicciones usando Rolling

ECM usando Rolling

Predicción 5 pasos adelante

Comparación

Dep. Variable:	y	No. Observations:	1465
Model:	SARIMAX(2, 1, 2)	Log Likelihood	-1402.617
Date:	Wed, 23 Nov 2022	AIC	2815.234
Time:	01:33:04	BIC	2841.678
Sample:	01-01-2017	HQIC	2825.097
	- 01-04-2021
Covariance Type:	opg

Ljung-Box (L1) (Q):	0.01	Jarque-Bera (JB):	814.33
Prob(Q):	0.91	Prob(JB):	0.00
Heteroskedasticity (H):	0.85	Skew:	0.12
Prob(H) (two-sided):	0.07	Kurtosis:	6.65